TSTP Solution File: SWW473+5 by cvc5---1.0.5
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- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SWW473+5 : TPTP v8.1.2. Released v5.3.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n014.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 1 00:21:06 EDT 2023
% Result : Theorem 0.89s 1.11s
% Output : Proof 0.89s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.15/0.16 % Problem : SWW473+5 : TPTP v8.1.2. Released v5.3.0.
% 0.15/0.17 % Command : do_cvc5 %s %d
% 0.16/0.38 % Computer : n014.cluster.edu
% 0.16/0.38 % Model : x86_64 x86_64
% 0.16/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.38 % Memory : 8042.1875MB
% 0.16/0.38 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.38 % CPULimit : 300
% 0.16/0.38 % WCLimit : 300
% 0.16/0.38 % DateTime : Sun Aug 27 20:22:16 EDT 2023
% 0.16/0.38 % CPUTime :
% 0.23/0.54 %----Proving TF0_NAR, FOF, or CNF
% 0.89/1.11 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.wlalorg0aW/cvc5---1.0.5_10117.p...
% 0.89/1.11 ------- get file name : TPTP file name is SWW473+5
% 0.89/1.11 ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_10117.smt2...
% 0.89/1.11 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.89/1.11 % SZS status Theorem for SWW473+5
% 0.89/1.11 % SZS output start Proof for SWW473+5
% 0.89/1.11 (
% 0.89/1.11 (let ((_let_1 (tptp.fun tptp.x_a tptp.bool))) (let ((_let_2 (tptp.fun tptp.pname tptp.bool))) (let ((_let_3 (tptp.fun tptp.pname tptp.x_a))) (let ((_let_4 (tptp.hAPP _let_2 _let_1 (tptp.hAPP _let_3 (tptp.fun _let_2 _let_1) (tptp.image tptp.pname tptp.x_a) tptp.mgt_call) tptp.u))) (let ((_let_5 (tptp.hAPP tptp.pname tptp.x_a tptp.mgt_call tptp.pn))) (let ((_let_6 (tptp.ord_less_eq _let_1))) (let ((_let_7 (tptp.fun _let_1 tptp.bool))) (let ((_let_8 (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_7 _let_6 (tptp.hAPP _let_1 _let_1 (tptp.hAPP tptp.x_a (tptp.fun _let_1 _let_1) (tptp.insert tptp.x_a) _let_5) tptp.g)) _let_4)))) (let ((_let_9 (not _let_8))) (let ((_let_10 (tptp.hAPP tptp.x_a _let_7 (tptp.member tptp.x_a) _let_5))) (let ((_let_11 (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP tptp.pname (tptp.fun _let_2 tptp.bool) (tptp.member tptp.pname) tptp.pn) tptp.u)))) (let ((_let_12 (tptp.hAPP tptp.nat tptp.nat tptp.suc tptp.na))) (let ((_let_13 (tptp.finite_card tptp.x_a))) (let ((_let_14 (tptp.hAPP _let_1 tptp.nat _let_13 _let_4))) (let ((_let_15 (tptp.minus_minus tptp.nat))) (let ((_let_16 (tptp.fun tptp.nat tptp.nat))) (let ((_let_17 (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_7 _let_6 tptp.g) _let_4)))) (let ((_let_18 (forall ((X_b $$unsorted) (X_2 $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.ord_less_eq _let_1))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (= (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_3 _let_2 (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b (tptp.fun _let_1 _let_1) (tptp.insert X_b) X_2) A_1)) B)) (and (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b _let_3 (tptp.member X_b) X_2) B)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_3 _let_2 A_1) B)))))))))) (let ((_let_19 (forall ((X_c $$unsorted) (X_b $$unsorted) (F $$unsorted) (X_2 $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.fun X_c tptp.bool))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP X_b (tptp.fun _let_2 tptp.bool) (tptp.member X_b) X_2) A_1)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_c (tptp.fun _let_1 tptp.bool) (tptp.member X_c) (tptp.hAPP X_b X_c F X_2)) (tptp.hAPP _let_2 _let_1 (tptp.hAPP (tptp.fun X_b X_c) (tptp.fun _let_2 _let_1) (tptp.image X_b X_c) F) A_1))))))))) (let ((_let_20 (tptp.fun tptp.bool tptp.bool))) (let ((_let_21 (tptp.fun tptp.bool _let_20))) (let ((_let_22 (forall ((X_c $$unsorted) (X_b $$unsorted) (F $$unsorted) (X_2 $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.fun X_c tptp.bool))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (or (not (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP X_b (tptp.fun _let_2 tptp.bool) (tptp.member X_b) X_2) A_1))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_c (tptp.fun _let_1 tptp.bool) (tptp.member X_c) (tptp.hAPP X_b X_c F X_2)) (tptp.hAPP _let_2 _let_1 (tptp.hAPP (tptp.fun X_b X_c) (tptp.fun _let_2 _let_1) (tptp.image X_b X_c) F) A_1))))))))) (let ((_let_23 (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_10 _let_4)))) (let ((_let_24 (not _let_11))) (let ((_let_25 (or _let_24 _let_23))) (let ((_let_26 (EQ_RESOLVE (ASSUME :args (_let_19)) (MACRO_SR_EQ_INTRO :args (_let_19 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_27 (not _let_25))) (let ((_let_28 (and _let_23 _let_17))) (let ((_let_29 (not _let_23))) (let ((_let_30 (= _let_8 _let_28))) (let ((_let_31 (not _let_28))) (let ((_let_32 (_let_18))) (let ((_let_33 (ASSUME :args _let_32))) (let ((_let_34 (tptp.fun X_b tptp.bool))) (let ((_let_35 (tptp.fun X_c tptp.bool))) (let ((_let_36 (tptp.fun X_b tptp.bool))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_26 :args (tptp.x_a tptp.pname tptp.mgt_call tptp.pn tptp.u QUANTIFIERS_INST_E_MATCHING ((tptp.hAPP _let_35 tptp.bool (tptp.hAPP X_c (tptp.fun _let_35 tptp.bool) (tptp.member X_c) (tptp.hAPP X_b X_c F X_2)) (tptp.hAPP _let_36 _let_35 (tptp.hAPP (tptp.fun X_b X_c) (tptp.fun _let_36 _let_35) (tptp.image X_b X_c) F) A_1))))) :args (_let_22))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_25)) :args ((or _let_24 _let_23 _let_27))) (ASSUME :args (_let_11)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_NEG :args (_let_28)) :args ((or (not _let_17) _let_28 _let_29))) (ASSUME :args (_let_17)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_30)) :args ((or _let_8 _let_31 (not _let_30)))) (ASSUME :args (_let_9)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_33 :args (tptp.x_a _let_5 tptp.g _let_4 QUANTIFIERS_INST_E_MATCHING ((tptp.hAPP _let_34 tptp.bool (tptp.hAPP _let_34 (tptp.fun _let_34 tptp.bool) (tptp.ord_less_eq _let_34) (tptp.hAPP _let_34 _let_34 (tptp.hAPP X_b (tptp.fun _let_34 _let_34) (tptp.insert X_b) X_2) A_1)) B)))) :args _let_32)) _let_33 :args (_let_30 false _let_18)) :args (_let_31 true _let_8 false _let_30)) :args (_let_29 false _let_17 true _let_28)) :args (_let_27 false _let_11 true _let_23)) _let_26 :args (false true _let_25 false _let_22)) :args ((forall ((X_b $$unsorted) (X_c $$unsorted) (X_a $$unsorted)) (let ((_let_1 (tptp.combb X_b X_c X_a))) (= (tptp.ti (tptp.fun (tptp.fun X_b X_c) (tptp.fun (tptp.fun X_a X_b) (tptp.fun X_a X_c))) _let_1) _let_1))) (forall ((X_a $$unsorted) (X_b $$unsorted) (X_c $$unsorted)) (let ((_let_1 (tptp.combc X_a X_b X_c))) (= (tptp.ti (tptp.fun (tptp.fun X_a (tptp.fun X_b X_c)) (tptp.fun X_b (tptp.fun X_a X_c))) _let_1) _let_1))) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.combi X_a))) (= (tptp.ti (tptp.fun X_a X_a) _let_1) _let_1))) (forall ((X_a $$unsorted) (X_b $$unsorted) (X_c $$unsorted)) (let ((_let_1 (tptp.combs X_a X_b X_c))) (= (tptp.ti (tptp.fun (tptp.fun X_a (tptp.fun X_b X_c)) (tptp.fun (tptp.fun X_a X_b) (tptp.fun X_a X_c))) _let_1) _let_1))) (forall ((X_c $$unsorted)) (let ((_let_1 (tptp.finite_card X_c))) (= (tptp.ti (tptp.fun (tptp.fun X_c tptp.bool) tptp.nat) _let_1) _let_1))) (forall ((X_b $$unsorted)) (let ((_let_1 (tptp.finite_finite X_b))) (= (tptp.ti (tptp.fun (tptp.fun X_b tptp.bool) tptp.bool) _let_1) _let_1))) (= (tptp.ti (tptp.fun tptp.nat _let_16) _let_15) _let_15) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.undefined X_a))) (= (tptp.ti X_a _let_1) _let_1))) (= (tptp.ti _let_16 tptp.suc) tptp.suc) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.ord_less_eq X_a))) (=> (tptp.preorder X_a) (= (tptp.ti (tptp.fun X_a (tptp.fun X_a tptp.bool)) _let_1) _let_1)))) (forall ((X_b $$unsorted)) (let ((_let_1 (tptp.collect X_b))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (= (tptp.ti (tptp.fun _let_2 _let_2) _let_1) _let_1)))) (forall ((X_b $$unsorted) (X_c $$unsorted)) (let ((_let_1 (tptp.image X_b X_c))) (= (tptp.ti (tptp.fun (tptp.fun X_b X_c) (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_c tptp.bool))) _let_1) _let_1))) (forall ((X_b $$unsorted)) (let ((_let_1 (tptp.insert X_b))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (= (tptp.ti (tptp.fun X_b (tptp.fun _let_2 _let_2)) _let_1) _let_1)))) (= (tptp.ti _let_20 tptp.fNot) tptp.fNot) (= (tptp.ti _let_21 tptp.fconj) tptp.fconj) (= (tptp.ti _let_21 tptp.fdisj) tptp.fdisj) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.fequal X_a))) (= (tptp.ti (tptp.fun X_a (tptp.fun X_a tptp.bool)) _let_1) _let_1))) (= (tptp.ti _let_21 tptp.fimplies) tptp.fimplies) (forall ((X_a $$unsorted) (X_c $$unsorted) (B_1_1 $$unsorted) (B_2 $$unsorted)) (= (tptp.hAPP X_a X_c (tptp.ti (tptp.fun X_a X_c) B_1_1) B_2) (tptp.hAPP X_a X_c B_1_1 B_2))) (forall ((X_a $$unsorted) (X_c $$unsorted) (B_1_1 $$unsorted) (B_2 $$unsorted)) (= (tptp.hAPP X_a X_c B_1_1 (tptp.ti X_a B_2)) (tptp.hAPP X_a X_c B_1_1 B_2))) (forall ((X_c $$unsorted) (X_a $$unsorted) (B_1_1 $$unsorted) (B_2 $$unsorted)) (let ((_let_1 (tptp.hAPP X_a X_c B_1_1 B_2))) (= (tptp.ti X_c _let_1) _let_1))) (forall ((B_1_1 $$unsorted)) (= (tptp.hBOOL (tptp.ti tptp.bool B_1_1)) (tptp.hBOOL B_1_1))) (forall ((X_b $$unsorted)) (let ((_let_1 (tptp.member X_b))) (= (tptp.ti (tptp.fun X_b (tptp.fun (tptp.fun X_b tptp.bool) tptp.bool)) _let_1) _let_1))) (= (tptp.ti _let_1 tptp.g) tptp.g) (= (tptp.ti (tptp.fun _let_1 _let_7) tptp.p) tptp.p) (= (tptp.ti _let_2 tptp.u) tptp.u) (= (tptp.ti _let_3 tptp.mgt_call) tptp.mgt_call) (= (tptp.ti tptp.nat tptp.na) tptp.na) (= (tptp.ti tptp.pname tptp.pn) tptp.pn) (forall ((Ts $$unsorted) (G_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.x_a tptp.bool))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_2 (tptp.ord_less_eq _let_1) Ts) G_1)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_2 tptp.p G_1) Ts)))))) (forall ((X_b $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.fun _let_1 _let_2))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite X_b) A_1)) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.finite_finite _let_1) (tptp.hAPP _let_2 _let_2 (tptp.collect _let_1) (tptp.hAPP _let_1 _let_2 (tptp.hAPP _let_3 _let_3 (tptp.combc _let_1 _let_1 tptp.bool) (tptp.ord_less_eq _let_1)) A_1))))))))) (forall ((X_c $$unsorted) (X_b $$unsorted) (H $$unsorted) (F_1 $$unsorted)) (let ((_let_1 (tptp.fun X_c tptp.bool))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.finite_finite X_b) F_1)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite X_c) (tptp.hAPP _let_2 _let_1 (tptp.hAPP (tptp.fun X_b X_c) (tptp.fun _let_2 _let_1) (tptp.image X_b X_c) H) F_1))))))) (forall ((X_b $$unsorted) (A_2 $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.finite_finite X_b))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 A_1)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b (tptp.fun _let_1 _let_1) (tptp.insert X_b) A_2) A_1))))))) (forall ((X_c $$unsorted) (X_b $$unsorted) (F $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun X_c tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite X_b) A_1)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) (tptp.hAPP _let_2 tptp.nat (tptp.finite_card X_c) (tptp.hAPP _let_1 _let_2 (tptp.hAPP (tptp.fun X_b X_c) (tptp.fun _let_1 _let_2) (tptp.image X_b X_c) F) A_1))) (tptp.hAPP _let_1 tptp.nat (tptp.finite_card X_b) A_1))))))) (forall ((X_b $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.finite_card X_b))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.finite_finite X_b) B)) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_2 (tptp.fun _let_2 tptp.bool) (tptp.ord_less_eq _let_2) A_1) B)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) (tptp.hAPP _let_2 tptp.nat _let_1 A_1)) (tptp.hAPP _let_2 tptp.nat _let_1 B)))))))) (forall ((X_b $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.finite_card X_b))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite X_b) B)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_1 tptp.bool) (tptp.ord_less_eq _let_1) A_1) B)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) (tptp.hAPP _let_1 tptp.nat _let_2 B)) (tptp.hAPP _let_1 tptp.nat _let_2 A_1))) (= (tptp.ti _let_1 A_1) (tptp.ti _let_1 B)))))))) (forall ((X_b $$unsorted) (X_2 $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.finite_card X_b))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite X_b) A_1)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) (tptp.hAPP _let_1 tptp.nat _let_2 A_1)) (tptp.hAPP _let_1 tptp.nat _let_2 (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b (tptp.fun _let_1 _let_1) (tptp.insert X_b) X_2) A_1)))))))) (forall ((X_b $$unsorted) (X_2 $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.finite_card X_b))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (let ((_let_3 (tptp.hAPP _let_2 tptp.nat _let_1 A_1))) (let ((_let_4 (tptp.hAPP _let_2 tptp.nat _let_1 (tptp.hAPP _let_2 _let_2 (tptp.hAPP X_b (tptp.fun _let_2 _let_2) (tptp.insert X_b) X_2) A_1)))) (let ((_let_5 (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP X_b (tptp.fun _let_2 tptp.bool) (tptp.member X_b) X_2) A_1)))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.finite_finite X_b) A_1)) (and (=> _let_5 (= _let_4 _let_3)) (=> (not _let_5) (= _let_4 (tptp.hAPP tptp.nat tptp.nat tptp.suc _let_3))))))))))) (forall ((X_b $$unsorted) (X_2 $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.finite_card X_b))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.finite_finite X_b) A_1)) (=> (not (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP X_b (tptp.fun _let_2 tptp.bool) (tptp.member X_b) X_2) A_1))) (= (tptp.hAPP _let_2 tptp.nat _let_1 (tptp.hAPP _let_2 _let_2 (tptp.hAPP X_b (tptp.fun _let_2 _let_2) (tptp.insert X_b) X_2) A_1)) (tptp.hAPP tptp.nat tptp.nat tptp.suc (tptp.hAPP _let_2 tptp.nat _let_1 A_1)))))))) (forall ((X_b $$unsorted) (Q_1 $$unsorted) (Pa $$unsorted)) (let ((_let_1 (tptp.fun tptp.bool tptp.bool))) (let ((_let_2 (tptp.fun X_b _let_1))) (let ((_let_3 (tptp.fun X_b tptp.bool))) (let ((_let_4 (tptp.collect X_b))) (let ((_let_5 (tptp.finite_finite X_b))) (=> (or (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool _let_5 (tptp.hAPP _let_3 _let_3 _let_4 Pa))) (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool _let_5 (tptp.hAPP _let_3 _let_3 _let_4 Q_1)))) (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool _let_5 (tptp.hAPP _let_3 _let_3 _let_4 (tptp.hAPP _let_3 _let_3 (tptp.hAPP _let_2 (tptp.fun _let_3 _let_3) (tptp.combs X_b tptp.bool tptp.bool) (tptp.hAPP _let_3 _let_2 (tptp.hAPP (tptp.fun tptp.bool _let_1) (tptp.fun _let_3 _let_2) (tptp.combb tptp.bool _let_1 X_b) tptp.fconj) Pa)) Q_1))))))))))) (forall ((N_1 $$unsorted) (M_2 $$unsorted)) (let ((_let_1 (tptp.minus_minus tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.nat))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) N_1) M_2)) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat tptp.suc M_2)) N_1) (tptp.hAPP tptp.nat tptp.nat tptp.suc (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 M_2) N_1))))))) (forall ((K $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (let ((_let_2 (tptp.fun tptp.nat _let_1))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite tptp.nat) (tptp.hAPP _let_1 _let_1 (tptp.collect tptp.nat) (tptp.hAPP tptp.nat _let_1 (tptp.hAPP _let_2 _let_2 (tptp.combc tptp.nat tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat)) K))))))) (forall ((Na $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (let ((_let_2 (tptp.fun tptp.nat _let_1))) (= (tptp.hAPP _let_1 tptp.nat (tptp.finite_card tptp.nat) (tptp.hAPP _let_1 _let_1 (tptp.collect tptp.nat) (tptp.hAPP tptp.nat _let_1 (tptp.hAPP _let_2 _let_2 (tptp.combc tptp.nat tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat)) Na))) (tptp.hAPP tptp.nat tptp.nat tptp.suc Na))))) (forall ((X_b $$unsorted)) (=> (tptp.finite_finite_1 X_b) (forall ((A_1 $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.finite_finite X_b) A_1))))) (forall ((X_b $$unsorted)) (=> (tptp.finite_finite_1 X_b) (forall ((A_1 $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.finite_finite X_b) A_1))))) (forall ((X $$unsorted) (Y $$unsorted)) (=> (= (tptp.hAPP tptp.nat tptp.nat tptp.suc X) (tptp.hAPP tptp.nat tptp.nat tptp.suc Y)) (= X Y))) (forall ((Nat_1 $$unsorted) (Nat $$unsorted)) (= (= (tptp.hAPP tptp.nat tptp.nat tptp.suc Nat_1) (tptp.hAPP tptp.nat tptp.nat tptp.suc Nat)) (= Nat_1 Nat))) (forall ((N_1 $$unsorted)) (not (= (tptp.hAPP tptp.nat tptp.nat tptp.suc N_1) N_1))) (forall ((N_1 $$unsorted)) (not (= N_1 (tptp.hAPP tptp.nat tptp.nat tptp.suc N_1)))) (forall ((M_2 $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.ord_less_eq tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 M_2) N_1)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 N_1) M_2)) (= M_2 N_1)))))) (forall ((K_1 $$unsorted) (I_1 $$unsorted) (J $$unsorted)) (let ((_let_1 (tptp.ord_less_eq tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (let ((_let_3 (tptp.hAPP tptp.nat _let_2 _let_1 I_1))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_3 J)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 J) K_1)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_3 K_1)))))))) (forall ((M_2 $$unsorted) (N_1 $$unsorted)) (=> (= M_2 N_1) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) M_2) N_1)))) (forall ((M_2 $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.ord_less_eq tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (or (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 M_2) N_1)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 N_1) M_2)))))) (forall ((N_1 $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) N_1) N_1))) (forall ((I_1 $$unsorted) (J $$unsorted) (K_1 $$unsorted)) (let ((_let_1 (tptp.minus_minus tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.nat))) (let ((_let_3 (tptp.hAPP tptp.nat _let_2 _let_1 I_1))) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat _let_3 J)) K_1) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat _let_3 K_1)) J)))))) (forall ((X_b $$unsorted) (Pa $$unsorted) (Q_1 $$unsorted)) (let ((_let_1 (tptp.collect X_b))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (let ((_let_3 (tptp.finite_finite X_b))) (let ((_let_4 (tptp.fun tptp.bool tptp.bool))) (let ((_let_5 (tptp.fun X_b _let_4))) (= (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_3 (tptp.hAPP _let_2 _let_2 _let_1 (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_5 (tptp.fun _let_2 _let_2) (tptp.combs X_b tptp.bool tptp.bool) (tptp.hAPP _let_2 _let_5 (tptp.hAPP (tptp.fun tptp.bool _let_4) (tptp.fun _let_2 _let_5) (tptp.combb tptp.bool _let_4 X_b) tptp.fdisj) Pa)) Q_1)))) (and (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_3 (tptp.hAPP _let_2 _let_2 _let_1 Pa))) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_3 (tptp.hAPP _let_2 _let_2 _let_1 Q_1))))))))))) (forall ((X_b $$unsorted) (A_2 $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.finite_finite X_b))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (= (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_1 (tptp.hAPP _let_2 _let_2 (tptp.hAPP X_b (tptp.fun _let_2 _let_2) (tptp.insert X_b) A_2) A_1))) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_1 A_1)))))) (forall ((X_b $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.finite_finite X_b))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_2 (tptp.fun _let_2 tptp.bool) (tptp.ord_less_eq _let_2) A_1) B)) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_1 B)) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_1 A_1))))))) (forall ((X_b $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.finite_finite X_b))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_1 B)) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_2 (tptp.fun _let_2 tptp.bool) (tptp.ord_less_eq _let_2) A_1) B)) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_1 A_1))))))) (forall ((M_2 $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.ord_less_eq tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat tptp.suc M_2)) N_1)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 M_2) N_1)))))) (forall ((M_2 $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat tptp.nat tptp.suc N_1))) (let ((_let_2 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) M_2))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_2 _let_1)) (=> (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_2 N_1))) (= M_2 _let_1)))))) (forall ((M_2 $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) M_2))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 N_1)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 (tptp.hAPP tptp.nat tptp.nat tptp.suc N_1)))))) (forall ((Na $$unsorted) (M_3 $$unsorted)) (let ((_let_1 (tptp.ord_less_eq tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat tptp.suc Na)) (tptp.hAPP tptp.nat tptp.nat tptp.suc M_3))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 Na) M_3)))))) (forall ((M_3 $$unsorted) (Na $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat tptp.nat tptp.suc Na))) (let ((_let_2 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) M_3))) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_2 _let_1)) (or (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_2 Na)) (= M_3 _let_1)))))) (forall ((M_3 $$unsorted) (Na $$unsorted)) (let ((_let_1 (tptp.ord_less_eq tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (= (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 M_3) Na))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat tptp.suc Na)) M_3)))))) (forall ((N_1 $$unsorted)) (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) (tptp.hAPP tptp.nat tptp.nat tptp.suc N_1)) N_1)))) (forall ((M_2 $$unsorted) (N_1 $$unsorted) (K_1 $$unsorted)) (let ((_let_1 (tptp.minus_minus tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.nat))) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat tptp.suc M_2)) N_1)) (tptp.hAPP tptp.nat tptp.nat tptp.suc K_1)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 M_2) N_1)) K_1))))) (forall ((M_2 $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.minus_minus tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.nat))) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat tptp.suc M_2)) (tptp.hAPP tptp.nat tptp.nat tptp.suc N_1)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 M_2) N_1))))) (forall ((Na $$unsorted) (K $$unsorted) (M_3 $$unsorted)) (let ((_let_1 (tptp.ord_less_eq tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (let ((_let_3 (tptp.minus_minus tptp.nat))) (let ((_let_4 (tptp.fun tptp.nat tptp.nat))) (let ((_let_5 (tptp.hAPP tptp.nat _let_2 _let_1 K))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_5 M_3)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_5 Na)) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_4 _let_3 M_3) K)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_4 _let_3 Na) K))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 M_3) Na))))))))))) (forall ((N_1 $$unsorted) (K_1 $$unsorted) (M_2 $$unsorted)) (let ((_let_1 (tptp.minus_minus tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.nat))) (let ((_let_3 (tptp.hAPP tptp.nat _let_2 _let_1 M_2))) (let ((_let_4 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) K_1))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_4 M_2)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_4 N_1)) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat _let_3 K_1)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 N_1) K_1)) (tptp.hAPP tptp.nat tptp.nat _let_3 N_1))))))))) (forall ((Na $$unsorted) (K $$unsorted) (M_3 $$unsorted)) (let ((_let_1 (tptp.minus_minus tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.nat))) (let ((_let_3 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) K))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_3 M_3)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_3 Na)) (= (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 M_3) K) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 Na) K)) (= M_3 Na)))))))) (forall ((I_1 $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.minus_minus tptp.nat) N_1))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) I_1) N_1)) (= (tptp.hAPP tptp.nat tptp.nat _let_1 (tptp.hAPP tptp.nat tptp.nat _let_1 I_1)) I_1)))) (forall ((L $$unsorted) (M_2 $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.minus_minus tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.nat))) (let ((_let_3 (tptp.ord_less_eq tptp.nat))) (let ((_let_4 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_4 _let_3 M_2) N_1)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_4 _let_3 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 M_2) L)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 N_1) L))))))))) (forall ((L $$unsorted) (M_2 $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.minus_minus tptp.nat) L))) (let ((_let_2 (tptp.ord_less_eq tptp.nat))) (let ((_let_3 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_3 _let_2 M_2) N_1)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_3 _let_2 (tptp.hAPP tptp.nat tptp.nat _let_1 N_1)) (tptp.hAPP tptp.nat tptp.nat _let_1 M_2)))))))) (forall ((M_2 $$unsorted) (N_1 $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.minus_minus tptp.nat) M_2) N_1)) M_2))) (forall ((X_c $$unsorted) (X_b $$unsorted) (B $$unsorted) (F $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.fun X_c tptp.bool))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.finite_finite X_b) A_1)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_1 tptp.bool) (tptp.ord_less_eq _let_1) B) (tptp.hAPP _let_2 _let_1 (tptp.hAPP (tptp.fun X_b X_c) (tptp.fun _let_2 _let_1) (tptp.image X_b X_c) F) A_1))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite X_c) B))))))) (forall ((X_c $$unsorted) (X_b $$unsorted) (F $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun X_c tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite X_b) B)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_1 tptp.bool) (tptp.ord_less_eq _let_1) B) (tptp.hAPP _let_2 _let_1 (tptp.hAPP (tptp.fun X_c X_b) (tptp.fun _let_2 _let_1) (tptp.image X_c X_b) F) A_1))) (exists ((C_2 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun X_c tptp.bool))) (and (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_2 (tptp.fun _let_2 tptp.bool) (tptp.ord_less_eq _let_2) C_2) A_1)) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.finite_finite X_c) C_2)) (= (tptp.ti _let_1 B) (tptp.hAPP _let_2 _let_1 (tptp.hAPP (tptp.fun X_c X_b) (tptp.fun _let_2 _let_1) (tptp.image X_c X_b) F) C_2))))))))))) (forall ((X_b $$unsorted)) (=> (tptp.order X_b) (forall ((Na $$unsorted) (N_3 $$unsorted) (F $$unsorted)) (=> (forall ((N_2 $$unsorted)) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b (tptp.fun X_b tptp.bool) (tptp.ord_less_eq X_b) (tptp.hAPP tptp.nat X_b F N_2)) (tptp.hAPP tptp.nat X_b F (tptp.hAPP tptp.nat tptp.nat tptp.suc N_2))))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) Na) N_3)) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b (tptp.fun X_b tptp.bool) (tptp.ord_less_eq X_b) (tptp.hAPP tptp.nat X_b F Na)) (tptp.hAPP tptp.nat X_b F N_3)))))))) (forall ((X_c $$unsorted) (X_b $$unsorted) (F $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.fun X_c tptp.bool))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (=> (not (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.finite_finite X_b) A_1))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite X_c) (tptp.hAPP _let_2 _let_1 (tptp.hAPP (tptp.fun X_b X_c) (tptp.fun _let_2 _let_1) (tptp.image X_b X_c) F) A_1))) (exists ((X_1 $$unsorted)) (let ((_let_1 (tptp.fun X_c tptp.bool))) (let ((_let_2 (tptp.fun X_b _let_1))) (let ((_let_3 (tptp.fun X_b X_c))) (let ((_let_4 (tptp.fun X_b tptp.bool))) (let ((_let_5 (tptp.member X_b))) (let ((_let_6 (tptp.fun _let_4 _let_4))) (let ((_let_7 (tptp.fun _let_4 tptp.bool))) (let ((_let_8 (tptp.fun tptp.bool tptp.bool))) (let ((_let_9 (tptp.fun X_b _let_8))) (and (tptp.hBOOL (tptp.hAPP _let_4 tptp.bool (tptp.hAPP X_b _let_7 _let_5 X_1) A_1)) (not (tptp.hBOOL (tptp.hAPP _let_4 tptp.bool (tptp.finite_finite X_b) (tptp.hAPP _let_4 _let_4 (tptp.collect X_b) (tptp.hAPP _let_4 _let_4 (tptp.hAPP _let_9 _let_6 (tptp.combs X_b tptp.bool tptp.bool) (tptp.hAPP _let_4 _let_9 (tptp.hAPP (tptp.fun tptp.bool _let_8) (tptp.fun _let_4 _let_9) (tptp.combb tptp.bool _let_8 X_b) tptp.fconj) (tptp.hAPP _let_4 _let_4 (tptp.hAPP (tptp.fun X_b _let_7) _let_6 (tptp.combc X_b _let_4 tptp.bool) _let_5) A_1))) (tptp.hAPP X_c _let_4 (tptp.hAPP _let_2 (tptp.fun X_c _let_4) (tptp.combc X_b X_c tptp.bool) (tptp.hAPP _let_3 _let_2 (tptp.hAPP (tptp.fun X_c _let_1) (tptp.fun _let_3 _let_2) (tptp.combb X_c _let_1 X_b) (tptp.fequal X_c)) F)) (tptp.hAPP X_b X_c F X_1))))))))))))))))))))))) (forall ((X_b $$unsorted) (X_c $$unsorted) (A_1 $$unsorted) (B_1 $$unsorted) (F $$unsorted) (X_2 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun X_c tptp.bool))) (=> (= (tptp.ti X_b B_1) (tptp.hAPP X_c X_b F X_2)) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP X_c (tptp.fun _let_2 tptp.bool) (tptp.member X_c) X_2) A_1)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) B_1) (tptp.hAPP _let_2 _let_1 (tptp.hAPP (tptp.fun X_c X_b) (tptp.fun _let_2 _let_1) (tptp.image X_c X_b) F) A_1)))))))) (forall ((X_b $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.ord_less_eq _let_1))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_3 _let_2 A_1) B)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_3 _let_2 B) A_1)) (= (tptp.ti _let_1 A_1) (tptp.ti _let_1 B)))))))) (forall ((X_b $$unsorted) (C_1 $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.hAPP X_b _let_2 (tptp.member X_b) C_1))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_2 (tptp.ord_less_eq _let_1) A_1) B)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_3 A_1)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_3 B)))))))) (forall ((X_b $$unsorted) (B_1 $$unsorted) (A_2 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) A_2))) (=> (=> (not (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 B))) (= (tptp.ti X_b A_2) (tptp.ti X_b B_1))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b (tptp.fun _let_1 _let_1) (tptp.insert X_b) B_1) B))))))) (forall ((X_b $$unsorted) (A_2 $$unsorted) (B_1 $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) A_2))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b (tptp.fun _let_1 _let_1) (tptp.insert X_b) B_1) A_1))) (=> (not (= (tptp.ti X_b A_2) (tptp.ti X_b B_1))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 A_1))))))) (forall ((X_b $$unsorted) (A_2 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) A_2) (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b (tptp.fun _let_1 _let_1) (tptp.insert X_b) A_2) B))))) (forall ((X_b $$unsorted) (A_2 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun _let_1 _let_1))) (let ((_let_3 (tptp.fun X_b _let_1))) (let ((_let_4 (tptp.fun tptp.bool tptp.bool))) (let ((_let_5 (tptp.fun X_b _let_4))) (= (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b _let_2 (tptp.insert X_b) A_2) B) (tptp.hAPP _let_1 _let_1 (tptp.collect X_b) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_5 _let_2 (tptp.combs X_b tptp.bool tptp.bool) (tptp.hAPP _let_1 _let_5 (tptp.hAPP (tptp.fun tptp.bool _let_4) (tptp.fun _let_1 _let_5) (tptp.combb tptp.bool _let_4 X_b) tptp.fdisj) (tptp.hAPP X_b _let_1 (tptp.hAPP _let_3 _let_3 (tptp.combc X_b X_b tptp.bool) (tptp.fequal X_b)) A_2))) (tptp.hAPP _let_1 _let_1 (tptp.hAPP (tptp.fun X_b (tptp.fun _let_1 tptp.bool)) _let_2 (tptp.combc X_b _let_1 tptp.bool) (tptp.member X_b)) B)))))))))) (forall ((X_b $$unsorted) (A_2 $$unsorted) (Pa $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun X_b _let_1))) (let ((_let_3 (tptp.fun _let_1 _let_1))) (let ((_let_4 (tptp.fun tptp.bool tptp.bool))) (let ((_let_5 (tptp.fun X_b _let_4))) (let ((_let_6 (tptp.collect X_b))) (= (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b _let_3 (tptp.insert X_b) A_2) (tptp.hAPP _let_1 _let_1 _let_6 Pa)) (tptp.hAPP _let_1 _let_1 _let_6 (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_5 _let_3 (tptp.combs X_b tptp.bool tptp.bool) (tptp.hAPP _let_1 _let_5 (tptp.hAPP (tptp.fun tptp.bool _let_4) (tptp.fun _let_1 _let_5) (tptp.combb tptp.bool _let_4 X_b) tptp.fimplies) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_4 _let_3 (tptp.combb tptp.bool tptp.bool X_b) tptp.fNot) (tptp.hAPP X_b _let_1 (tptp.hAPP _let_2 _let_2 (tptp.combc X_b X_b tptp.bool) (tptp.fequal X_b)) A_2)))) Pa)))))))))) (forall ((X_b $$unsorted) (X_2 $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.hAPP X_b (tptp.fun _let_1 _let_1) (tptp.insert X_b) X_2))) (let ((_let_3 (tptp.hAPP _let_1 _let_1 _let_2 A_1))) (= (tptp.hAPP _let_1 _let_1 _let_2 _let_3) _let_3))))) (forall ((X_b $$unsorted) (X_2 $$unsorted) (Y_2 $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.insert X_b))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (let ((_let_3 (tptp.fun _let_2 _let_2))) (let ((_let_4 (tptp.hAPP X_b _let_3 _let_1 X_2))) (let ((_let_5 (tptp.hAPP X_b _let_3 _let_1 Y_2))) (= (tptp.hAPP _let_2 _let_2 _let_4 (tptp.hAPP _let_2 _let_2 _let_5 A_1)) (tptp.hAPP _let_2 _let_2 _let_5 (tptp.hAPP _let_2 _let_2 _let_4 A_1))))))))) (forall ((X_b $$unsorted) (A_2 $$unsorted) (B_1 $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) A_2))) (= (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b (tptp.fun _let_1 _let_1) (tptp.insert X_b) B_1) A_1))) (or (= (tptp.ti X_b A_2) (tptp.ti X_b B_1)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 A_1))))))) (forall ((X_b $$unsorted) (Y_2 $$unsorted) (A_1 $$unsorted) (X_2 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (= (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b (tptp.fun _let_1 _let_1) (tptp.insert X_b) Y_2) A_1) X_2)) (or (= (tptp.ti X_b Y_2) (tptp.ti X_b X_2)) (tptp.hBOOL (tptp.hAPP X_b tptp.bool A_1 X_2)))))) (forall ((X_b $$unsorted) (B $$unsorted) (X_2 $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.hAPP X_b (tptp.fun _let_1 _let_1) (tptp.insert X_b) X_2))) (let ((_let_3 (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) X_2))) (=> (not (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_3 A_1))) (=> (not (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_3 B))) (= (= (tptp.hAPP _let_1 _let_1 _let_2 A_1) (tptp.hAPP _let_1 _let_1 _let_2 B)) (= (tptp.ti _let_1 A_1) (tptp.ti _let_1 B))))))))) (forall ((X_b $$unsorted) (B_1 $$unsorted) (A_2 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) A_2))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 B)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b (tptp.fun _let_1 _let_1) (tptp.insert X_b) B_1) B))))))) (forall ((X_b $$unsorted) (A_2 $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) A_2) A_1)) (= (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b (tptp.fun _let_1 _let_1) (tptp.insert X_b) A_2) A_1) (tptp.ti _let_1 A_1))))) (forall ((X_b $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_1 tptp.bool) (tptp.ord_less_eq _let_1) A_1) A_1)))) (forall ((X_b $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.ord_less_eq _let_1))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (= (= (tptp.ti _let_1 A_1) (tptp.ti _let_1 B)) (and (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_3 _let_2 A_1) B)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_3 _let_2 B) A_1)))))))) (forall ((X_b $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (=> (= (tptp.ti _let_1 A_1) (tptp.ti _let_1 B)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_1 tptp.bool) (tptp.ord_less_eq _let_1) A_1) B))))) (forall ((X_b $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (=> (= (tptp.ti _let_1 A_1) (tptp.ti _let_1 B)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_1 tptp.bool) (tptp.ord_less_eq _let_1) B) A_1))))) (forall ((X_b $$unsorted) (X_2 $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.hAPP X_b _let_2 (tptp.member X_b) X_2))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_2 (tptp.ord_less_eq _let_1) A_1) B)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_3 A_1)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_3 B)))))))) (forall ((X_b $$unsorted) (B $$unsorted) (X_2 $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.hAPP X_b _let_2 (tptp.member X_b) X_2))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_3 A_1)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_2 (tptp.ord_less_eq _let_1) A_1) B)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_3 B)))))))) (forall ((X_b $$unsorted) (X_2 $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.hAPP X_b _let_2 (tptp.member X_b) X_2))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_2 (tptp.ord_less_eq _let_1) A_1) B)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_3 A_1)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_3 B)))))))) (forall ((X_b $$unsorted) (C $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.ord_less_eq _let_1))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (let ((_let_4 (tptp.hAPP _let_1 _let_3 _let_2 A_1))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_4 B)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_3 _let_2 B) C)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_4 C))))))))) (forall ((X_b $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.ord_less_eq _let_1))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (=> (= (tptp.ti _let_1 A_1) (tptp.ti _let_1 B)) (not (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_3 _let_2 A_1) B)) (not (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_3 _let_2 B) A_1)))))))))) (forall ((X_b $$unsorted) (X_c $$unsorted) (F $$unsorted) (G $$unsorted)) (let ((_let_1 (tptp.fun X_b X_c))) (=> (forall ((X_1 $$unsorted)) (= (tptp.hAPP X_b X_c F X_1) (tptp.hAPP X_b X_c G X_1))) (= (tptp.ti _let_1 F) (tptp.ti _let_1 G))))) (forall ((X_b $$unsorted) (X_2 $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (= (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) X_2) A_1)) (tptp.hBOOL (tptp.hAPP X_b tptp.bool A_1 X_2))))) (forall ((X_b $$unsorted) (Pa $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (= (tptp.hAPP _let_1 _let_1 (tptp.collect X_b) Pa) (tptp.ti _let_1 Pa)))) (forall ((X_b $$unsorted) (X_c $$unsorted) (Z $$unsorted) (F $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun X_c tptp.bool))) (= (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) Z) (tptp.hAPP _let_2 _let_1 (tptp.hAPP (tptp.fun X_c X_b) (tptp.fun _let_2 _let_1) (tptp.image X_c X_b) F) A_1))) (exists ((X_1 $$unsorted)) (let ((_let_1 (tptp.fun X_c tptp.bool))) (and (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_c (tptp.fun _let_1 tptp.bool) (tptp.member X_c) X_1) A_1)) (= (tptp.ti X_b Z) (tptp.hAPP X_c X_b F X_1))))))))) _let_19 (forall ((X_c $$unsorted) (X_b $$unsorted) (B_1 $$unsorted) (F $$unsorted) (X_2 $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.fun X_c tptp.bool))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP X_b (tptp.fun _let_2 tptp.bool) (tptp.member X_b) X_2) A_1)) (=> (= (tptp.ti X_c B_1) (tptp.hAPP X_b X_c F X_2)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_c (tptp.fun _let_1 tptp.bool) (tptp.member X_c) B_1) (tptp.hAPP _let_2 _let_1 (tptp.hAPP (tptp.fun X_b X_c) (tptp.fun _let_2 _let_1) (tptp.image X_b X_c) F) A_1)))))))) (forall ((X_b $$unsorted) (X_1 $$unsorted) (Xa $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun _let_1 _let_1))) (let ((_let_3 (tptp.fun X_b _let_1))) (let ((_let_4 (tptp.fun tptp.bool tptp.bool))) (let ((_let_5 (tptp.fun X_b _let_4))) (= (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b _let_2 (tptp.insert X_b) X_1) Xa) (tptp.hAPP _let_1 _let_1 (tptp.collect X_b) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_5 _let_2 (tptp.combs X_b tptp.bool tptp.bool) (tptp.hAPP _let_1 _let_5 (tptp.hAPP (tptp.fun tptp.bool _let_4) (tptp.fun _let_1 _let_5) (tptp.combb tptp.bool _let_4 X_b) tptp.fdisj) (tptp.hAPP X_b _let_1 (tptp.hAPP _let_3 _let_3 (tptp.combc X_b X_b tptp.bool) (tptp.fequal X_b)) X_1))) (tptp.hAPP _let_1 _let_1 (tptp.hAPP (tptp.fun X_b (tptp.fun _let_1 tptp.bool)) _let_2 (tptp.combc X_b _let_1 tptp.bool) (tptp.member X_b)) Xa)))))))))) (forall ((X_c $$unsorted) (X_b $$unsorted) (X_d $$unsorted) (F $$unsorted) (G $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.fun X_d X_b))) (let ((_let_2 (tptp.fun X_d X_c))) (let ((_let_3 (tptp.fun X_c X_b))) (let ((_let_4 (tptp.fun X_b tptp.bool))) (let ((_let_5 (tptp.fun X_d tptp.bool))) (let ((_let_6 (tptp.fun X_c tptp.bool))) (= (tptp.hAPP _let_6 _let_4 (tptp.hAPP _let_3 (tptp.fun _let_6 _let_4) (tptp.image X_c X_b) F) (tptp.hAPP _let_5 _let_6 (tptp.hAPP _let_2 (tptp.fun _let_5 _let_6) (tptp.image X_d X_c) G) A_1)) (tptp.hAPP _let_5 _let_4 (tptp.hAPP _let_1 (tptp.fun _let_5 _let_4) (tptp.image X_d X_b) (tptp.hAPP _let_2 _let_1 (tptp.hAPP _let_3 (tptp.fun _let_2 _let_1) (tptp.combb X_c X_b X_d) F) G)) A_1))))))))) (forall ((X_b $$unsorted) (Y_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (= (tptp.hAPP _let_1 _let_1 (tptp.hAPP (tptp.fun X_b X_b) (tptp.fun _let_1 _let_1) (tptp.image X_b X_b) (tptp.combi X_b)) Y_1) (tptp.ti _let_1 Y_1)))) (forall ((X_b $$unsorted) (B $$unsorted) (A_2 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_1 tptp.bool) (tptp.ord_less_eq _let_1) B) (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b (tptp.fun _let_1 _let_1) (tptp.insert X_b) A_2) B))))) _let_18 (forall ((X_b $$unsorted) (B $$unsorted) (X_2 $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.hAPP _let_1 _let_2 (tptp.ord_less_eq _let_1) A_1))) (=> (not (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b _let_2 (tptp.member X_b) X_2) A_1))) (= (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_3 (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b (tptp.fun _let_1 _let_1) (tptp.insert X_b) X_2) B))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_3 B)))))))) (forall ((X_b $$unsorted) (B_1 $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.hAPP _let_1 (tptp.fun _let_1 tptp.bool) (tptp.ord_less_eq _let_1) A_1))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 B)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b (tptp.fun _let_1 _let_1) (tptp.insert X_b) B_1) B))))))) (forall ((X_b $$unsorted) (A_2 $$unsorted) (C $$unsorted) (D $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.hAPP X_b (tptp.fun _let_1 _let_1) (tptp.insert X_b) A_2))) (let ((_let_3 (tptp.ord_less_eq _let_1))) (let ((_let_4 (tptp.fun _let_1 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_4 _let_3 C) D)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_4 _let_3 (tptp.hAPP _let_1 _let_1 _let_2 C)) (tptp.hAPP _let_1 _let_1 _let_2 D))))))))) (forall ((X_c $$unsorted) (X_b $$unsorted) (F $$unsorted) (A_2 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun X_c tptp.bool))) (let ((_let_3 (tptp.hAPP (tptp.fun X_c X_b) (tptp.fun _let_2 _let_1) (tptp.image X_c X_b) F))) (= (tptp.hAPP _let_2 _let_1 _let_3 (tptp.hAPP _let_2 _let_2 (tptp.hAPP X_c (tptp.fun _let_2 _let_2) (tptp.insert X_c) A_2) B)) (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b (tptp.fun _let_1 _let_1) (tptp.insert X_b) (tptp.hAPP X_c X_b F A_2)) (tptp.hAPP _let_2 _let_1 _let_3 B))))))) (forall ((X_c $$unsorted) (X_b $$unsorted) (F $$unsorted) (X_2 $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.fun X_c tptp.bool))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (let ((_let_3 (tptp.hAPP _let_2 _let_1 (tptp.hAPP (tptp.fun X_b X_c) (tptp.fun _let_2 _let_1) (tptp.image X_b X_c) F) A_1))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP X_b (tptp.fun _let_2 tptp.bool) (tptp.member X_b) X_2) A_1)) (= (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_c (tptp.fun _let_1 _let_1) (tptp.insert X_c) (tptp.hAPP X_b X_c F X_2)) _let_3) _let_3)))))) (forall ((X_b $$unsorted) (X_c $$unsorted) (B $$unsorted) (F $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun X_c tptp.bool))) (= (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_1 tptp.bool) (tptp.ord_less_eq _let_1) B) (tptp.hAPP _let_2 _let_1 (tptp.hAPP (tptp.fun X_c X_b) (tptp.fun _let_2 _let_1) (tptp.image X_c X_b) F) A_1))) (exists ((AA $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun X_c tptp.bool))) (and (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_2 (tptp.fun _let_2 tptp.bool) (tptp.ord_less_eq _let_2) AA) A_1)) (= (tptp.ti _let_1 B) (tptp.hAPP _let_2 _let_1 (tptp.hAPP (tptp.fun X_c X_b) (tptp.fun _let_2 _let_1) (tptp.image X_c X_b) F) AA)))))))))) (forall ((X_c $$unsorted) (X_b $$unsorted) (F $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.fun X_c tptp.bool))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (let ((_let_3 (tptp.hAPP (tptp.fun X_b X_c) (tptp.fun _let_2 _let_1) (tptp.image X_b X_c) F))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_2 (tptp.fun _let_2 tptp.bool) (tptp.ord_less_eq _let_2) A_1) B)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_1 tptp.bool) (tptp.ord_less_eq _let_1) (tptp.hAPP _let_2 _let_1 _let_3 A_1)) (tptp.hAPP _let_2 _let_1 _let_3 B)))))))) (forall ((X_b $$unsorted) (X_c $$unsorted) (B_1 $$unsorted) (F $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun X_c tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) B_1) (tptp.hAPP _let_2 _let_1 (tptp.hAPP (tptp.fun X_c X_b) (tptp.fun _let_2 _let_1) (tptp.image X_c X_b) F) A_1))) (not (forall ((X_1 $$unsorted)) (let ((_let_1 (tptp.fun X_c tptp.bool))) (=> (= (tptp.ti X_b B_1) (tptp.hAPP X_c X_b F X_1)) (not (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_c (tptp.fun _let_1 tptp.bool) (tptp.member X_c) X_1) A_1))))))))))) (forall ((X_b $$unsorted) (B $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (=> (forall ((X_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) X_1))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 A_1)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 B)))))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_1 tptp.bool) (tptp.ord_less_eq _let_1) A_1) B))))) (forall ((I $$unsorted) (Pa $$unsorted) (K $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool Pa K)) (=> (forall ((N_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool Pa (tptp.hAPP tptp.nat tptp.nat tptp.suc N_2))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool Pa N_2)))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool Pa (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.minus_minus tptp.nat) K) I)))))) (forall ((N_1 $$unsorted) (M_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) (tptp.hAPP tptp.nat tptp.nat tptp.suc N_1)) M_1)) (exists ((M $$unsorted)) (= M_1 (tptp.hAPP tptp.nat tptp.nat tptp.suc M))))) (forall ((X_c $$unsorted) (X_b $$unsorted) (F $$unsorted) (B $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.fun X_c tptp.bool))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (=> (forall ((X_1 $$unsorted)) (let ((_let_1 (tptp.fun X_c tptp.bool))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP X_b (tptp.fun _let_2 tptp.bool) (tptp.member X_b) X_1) A_1)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_c (tptp.fun _let_1 tptp.bool) (tptp.member X_c) (tptp.hAPP X_b X_c F X_1)) B)))))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_1 tptp.bool) (tptp.ord_less_eq _let_1) (tptp.hAPP _let_2 _let_1 (tptp.hAPP (tptp.fun X_b X_c) (tptp.fun _let_2 _let_1) (tptp.image X_b X_c) F) A_1)) B)))))) (forall ((X_a $$unsorted)) (=> (tptp.preorder X_a) (forall ((X $$unsorted)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) X) X))))) (forall ((N $$unsorted)) (= (tptp.hBOOL (tptp.hAPP (tptp.fun tptp.nat tptp.bool) tptp.bool (tptp.finite_finite tptp.nat) N)) (exists ((M $$unsorted)) (forall ((X_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP tptp.nat (tptp.fun _let_1 tptp.bool) (tptp.member tptp.nat) X_1) N)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.ord_less_eq tptp.nat) X_1) M)))))))) (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (=> (tptp.preorder T_1) (tptp.preorder (tptp.fun T_2 T_1)))) (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (=> (and (tptp.finite_finite_1 T_1) (tptp.finite_finite_1 T_2)) (tptp.finite_finite_1 (tptp.fun T_2 T_1)))) (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (=> (tptp.order T_1) (tptp.order (tptp.fun T_2 T_1)))) (tptp.preorder tptp.nat) (tptp.order tptp.nat) (tptp.preorder tptp.bool) (tptp.finite_finite_1 tptp.bool) (tptp.order tptp.bool) (forall ((T $$unsorted) (A $$unsorted)) (let ((_let_1 (tptp.ti T A))) (= (tptp.ti T _let_1) _let_1))) (forall ((P $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP tptp.bool tptp.bool tptp.fNot P))) (not (tptp.hBOOL P)))) (forall ((P $$unsorted)) (or (tptp.hBOOL P) (tptp.hBOOL (tptp.hAPP tptp.bool tptp.bool tptp.fNot P)))) (forall ((X_a $$unsorted) (X_c $$unsorted) (X_b $$unsorted) (P $$unsorted) (Q $$unsorted) (R $$unsorted)) (let ((_let_1 (tptp.fun X_a X_c))) (let ((_let_2 (tptp.fun X_a X_b))) (= (tptp.hAPP X_a X_c (tptp.hAPP _let_2 _let_1 (tptp.hAPP (tptp.fun X_b X_c) (tptp.fun _let_2 _let_1) (tptp.combb X_b X_c X_a) P) Q) R) (tptp.hAPP X_b X_c P (tptp.hAPP X_a X_b Q R)))))) (forall ((X_a $$unsorted) (X_c $$unsorted) (X_b $$unsorted) (P $$unsorted) (Q $$unsorted) (R $$unsorted)) (let ((_let_1 (tptp.fun X_b X_c))) (let ((_let_2 (tptp.fun X_a X_c))) (= (tptp.hAPP X_a X_c (tptp.hAPP X_b _let_2 (tptp.hAPP (tptp.fun X_a _let_1) (tptp.fun X_b _let_2) (tptp.combc X_a X_b X_c) P) Q) R) (tptp.hAPP X_b X_c (tptp.hAPP X_a _let_1 P R) Q))))) (forall ((X_a $$unsorted) (P $$unsorted)) (= (tptp.hAPP X_a X_a (tptp.combi X_a) P) (tptp.ti X_a P))) (forall ((X_a $$unsorted) (X_c $$unsorted) (X_b $$unsorted) (P $$unsorted) (Q $$unsorted) (R $$unsorted)) (let ((_let_1 (tptp.fun X_b X_c))) (let ((_let_2 (tptp.fun X_a X_c))) (let ((_let_3 (tptp.fun X_a X_b))) (= (tptp.hAPP X_a X_c (tptp.hAPP _let_3 _let_2 (tptp.hAPP (tptp.fun X_a _let_1) (tptp.fun _let_3 _let_2) (tptp.combs X_a X_b X_c) P) Q) R) (tptp.hAPP X_b X_c (tptp.hAPP X_a _let_1 P R) (tptp.hAPP X_a X_b Q R))))))) (forall ((Q $$unsorted) (P $$unsorted)) (or (not (tptp.hBOOL P)) (not (tptp.hBOOL Q)) (tptp.hBOOL (tptp.hAPP tptp.bool tptp.bool (tptp.hAPP tptp.bool (tptp.fun tptp.bool tptp.bool) tptp.fconj P) Q)))) (forall ((P $$unsorted) (Q $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP tptp.bool tptp.bool (tptp.hAPP tptp.bool (tptp.fun tptp.bool tptp.bool) tptp.fconj P) Q))) (tptp.hBOOL P))) (forall ((P $$unsorted) (Q $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP tptp.bool tptp.bool (tptp.hAPP tptp.bool (tptp.fun tptp.bool tptp.bool) tptp.fconj P) Q))) (tptp.hBOOL Q))) (forall ((Q $$unsorted) (P $$unsorted)) (or (not (tptp.hBOOL P)) (tptp.hBOOL (tptp.hAPP tptp.bool tptp.bool (tptp.hAPP tptp.bool (tptp.fun tptp.bool tptp.bool) tptp.fdisj P) Q)))) (forall ((P $$unsorted) (Q $$unsorted)) (or (not (tptp.hBOOL Q)) (tptp.hBOOL (tptp.hAPP tptp.bool tptp.bool (tptp.hAPP tptp.bool (tptp.fun tptp.bool tptp.bool) tptp.fdisj P) Q)))) (forall ((P $$unsorted) (Q $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP tptp.bool tptp.bool (tptp.hAPP tptp.bool (tptp.fun tptp.bool tptp.bool) tptp.fdisj P) Q))) (tptp.hBOOL P) (tptp.hBOOL Q))) (forall ((X_a $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.fequal X_a) X) Y))) (= (tptp.ti X_a X) (tptp.ti X_a Y)))) (forall ((X_a $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (= (tptp.ti X_a X) (tptp.ti X_a Y))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.fequal X_a) X) Y)))) (forall ((Q $$unsorted) (P $$unsorted)) (or (tptp.hBOOL P) (tptp.hBOOL (tptp.hAPP tptp.bool tptp.bool (tptp.hAPP tptp.bool (tptp.fun tptp.bool tptp.bool) tptp.fimplies P) Q)))) (forall ((P $$unsorted) (Q $$unsorted)) (or (not (tptp.hBOOL Q)) (tptp.hBOOL (tptp.hAPP tptp.bool tptp.bool (tptp.hAPP tptp.bool (tptp.fun tptp.bool tptp.bool) tptp.fimplies P) Q)))) (forall ((P $$unsorted) (Q $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP tptp.bool tptp.bool (tptp.hAPP tptp.bool (tptp.fun tptp.bool tptp.bool) tptp.fimplies P) Q))) (not (tptp.hBOOL P)) (tptp.hBOOL Q))) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.finite_finite tptp.pname) tptp.u)) _let_17 (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) _let_12) _let_14)) (= (tptp.hAPP _let_1 tptp.nat _let_13 tptp.g) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_16 _let_15 _let_14) _let_12)) _let_11 (not (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_10 tptp.g))) _let_9 true)))))))))))))))))))))))))))))))))))))))
% 0.89/1.12 )
% 0.89/1.12 % SZS output end Proof for SWW473+5
% 0.89/1.12 % cvc5---1.0.5 exiting
% 0.89/1.12 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------